You should've used the word morha9a (مُرهَقة), ta3baana (تَعبانة) is only used in certain dialects and not in MSA.
No, مرهقة would better be translated "exhausted." متعبة (mut3aba[-tun]) is the word to use here.
My teacher is an Egyptian. He always uses the word "تعب" to express "tired".
"ta3ib" definitely works as well, but it feels a bit pretentious compared to "mut3ab."
Modern Standard Arabic
i think there is something wrong with the audio it says (Ahtaaaaye) that means it's plural it would be single if it's (Ahteeeeye)
Its supposed to be تعبة or متعبة and the audio for sister should be corrected
Does the statements "my sister is tired" and "my tired sister" differ in Arabic?
Yes, they do:
my sister is tired = أُختي مُرهَقة (Literally "My sister tired")
my tired sister = أُختي المُرهَقة (Literally "My sister the tired")
Ta3bana was ill right?
My tired is sister is the same a my sister is tired, right?
This is not correct, in classic Arabic, there is no word تَعْبانة, this word is from Egyptian dialect.
My sister is tired can be translated this way: أختي متعبة
Officially we say "تَعِبْ ومُتْعَبْ تعبة ومتعبة" this is the best and correct word and not "تعبان تعبانة" either if it is used.